PL19CH27-Grofman ARI 16 February 2016 14:5
R
E
V I E W
S
IN
A
D V A
N
CE
Perspectives on the
Comparative Study of
Electoral Systems
Bernard Grofman
Center for the Study of Democracy, School of Social Sciences, University of California,
Irvine, California 92697; email: BGTravel@uci.edu
Annu. Rev. Polit. Sci. 2016. 19:27.1–27.18
The Annual Review of Political Science is online at
polisci.annualreviews.org
This article’s doi:
10.1146/annurev-polisci-020614-092344
Copyright c 2016 by Annual Reviews.
All rights reserved
Keywords
electoral laws, electoral engineering, voting, elections, Duverger’s law,
proportionality
Abstract
This article considers the potential to use knowledge of expected electoral
system effects to engage in electoral engineering. The review focuses on
contributions made in the past dozen or so years and is limited to five specific
questions: How do electoral systems affect (a) the proportionality of seats–
votes relationships, (b) party proliferation, (c) the ideological nature of party
competition, (d ) voter turnout, and (e) the degree of match between the
preferences of citizens and the policy choices of the government?
27.1
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INTRODUCTION
Before the publication of Douglas Rae’s seminal Political Consequences of Electoral Law (1967), there
was a paucity of research on electoral rules, and much of that research was polemic in tone or
involved very abstract work on social choice aspects of voting procedures. Since then, the study
of electoral rules has become a central area of research within comparative politics—one whose
importance has continued to grow in recent decades. In particular, as emphasized by Htun &
Powell (2012a, p. 4),
Scores of political scientists have worked as consultants on missions to aspiring democracies designing
new institutions and to established ones contemplating electoral reform. They have offered “crash
courses” on electoral design to help policy makers and other stakeholders make informed decisions.
Political scientists have advised policy makers and other stakeholders about the consequences of adopting
particular configurations of electoral rules and regulations in specific places and at specific times
and offered recommendations to improve democratic performance in individual countries.
The study of electoral systems naturally lends itself to empirical analysis because many of its
central variables, such as vote shares and seat shares, are quantitative in nature. As the field matures,
the study of electoral systems has been enhanced because (a) there are many more countries with
a history of democratic elections to study; (b) new data sources, such as the Comparative Study of
Electoral Systems (CSES) project, have provided a mix of election data, survey data, and information
about the political context in which elections were held; (c) there are now archives of election
data available at the level of individual constituencies, not just aggregated at the national level;
(d ) the use of analytic tools, such as game theory, and of advanced statistical techniques has become
more common; and (e) the number of scholars involved in the subfield has grown enormously,
paralleling the dramatic growth in political science outside the English-speaking world.
For elections, we have quantifiable data over a multitude of cases, with substantial variation
in both dependent and independent variables of interest, as well as some long-run time-series
datawith many observations. These data allow us to test our theories. We can make before-andafter
comparisons to study the consequences of changes in electoral laws in real-world settings,
and we can do experiments to examine electoral law effects.1
For these reasons, electoral systems
research has been a showcase for the best of political science. Indeed, electoral systems research is
probably the subfield with the greatest immediate potential to justify calling the study of politics a
science; it shows that political scientists can establish useful empirical generalizations and theories
that are not time and country bound. Electoral systems research is the converse of New York City
as described in the song “New York, New York”: If political science can’t make it there, it can’t
make it anywhere.
The IDEA (Institute for Democracy and Electoral Assistance) Handbook on Electoral System
Design, in its various editions (e.g., Reynolds et al. 2005), provides basic information about voting
rules around the world, as well as national case studies on the effects of electoral system choices (see
1
Carey & Hix (2012) emphasize the limits on our ability to use cross-sectional or pooled cross-sectional data to establish
causality. As A. Wuffle once put it (personal communication, Apr. 1, 1986), “Getting at causality with cross-sectional data is like
trying to tell time with a stopped watch.” Three attempts to deal with this issue are the use of natural experiments that involve
a before-and-after comparison of electoral rule changes (Giannetti & Grofman 2011), the use of matching methods (Persson
& Tabellini 2005, ch. 5), and the use of experimental methods. I call the reader’s attention to experimental work involving
comparisons with the two-round election rules used in France (e.g., Balinksi & Laraki 2010, Blais et al. 2013, Baujard et al.
2014; various chapters in Dolez et al. 2011), as well as the work of the MEDW EuroVote project (http://eurovoteplus.eu/)
jointly organized by the University of Montreal and McGill University. EuroVote gathered data from 28 European countries
in which voters were asked to vote using three different forms of proportional representation.
27.2 Grofman
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also Golder 2005, Reynolds & Steenbergen 2006). A number of other books in the past decade or so
have provided overviews and/or detailed country studies (Colomer 2004, Norris 2004, Gallagher
& Mitchell 2005, Klingemann 2009). More recently, the American Political Science Association
(APSA) commissioned papers by some leading political scientists to review the state of the art in
selected topics in the electoral systems subfield, resulting in the 2012 Report by the APSA Presidential
Task Force on Electoral Rules and Democratic Governance (Htun & Powell 2012b).
I identify five different research traditions within the electoral systems subfield (Grofman 2011),
although of course the lines between these different approaches often blur: social choice theory,
mainstream empirical research, rational choice and game-theoretic models, the social physics
perspective, and the embedded systems approach.
Some social choice approaches, in the spirit of Arrow (1963 [1951]), seek to characterize voting
rules in axiomatic form or study normative properties of voting rules, e.g., responsiveness to
changes in underlying voter preferences, or likelihood of choosing a candidate who can receive a
majority over all other candidates in head-to-head contest (known in this literature as Condorcet
efficiency). Other scholars employing a social choice approach are concerned about the structure
of individual preferences, e.g., the extent to which preferences have a particular form of unidimensionality
known as single-peakedness or satisfy other domain restrictions. Other social choice
scholars take a particular set of assumptions about the distribution of voter preferences and assess
the likelihood that different voting methods will yield the same outcome (Saari 2008).
Mainstream empirical research seeks to measure the effects of particular electoral rules, crossnationally
or across different units in the same polity, by techniques such as regressing an outcome
variable, e.g., (effective) number of political parties or measures of proportionality of seats–votes
relationships, against electoral system features and some set of control variables (see, e.g., Lijphart
1994, Norris 2004). Mainstream empirical research is characterized by both country-specific studies
and large-scale data analysis of both survey and aggregate data at the cross-national level.
Rational choice modeling emphasizes strategic behavior by voters and candidates/parties, making
extensive use of game theory. Customarily, results in rational choice models are in the form of
theorems about how electoral system effects, in equilibrium, are determined by the incentives different
rules provide for the behavior of voters and parties/candidates under different assumptions
about the motivations we ascribe to voters, and the utility functions (office seeking, policy seeking,
or some combination thereof) we ascribe to parties/candidates (see e.g., Cox 1997). However,
a “soft” form of rational choice modeling draws on the underlying ideas of behavior driven by
incentives and constraints without the formalism of theorem proving.
The social physics approach, associated with the work of Rein Taagepera (see Taagepera &
Shugart 1989, and especially Taagepera 2007, 2008) is inspired by statistical thermodynamics in
physics. It does not attempt to predict the effects of electoral rules in individual political units
but seeks instead to precisely model effects on average. Although Taagepera has had a number of
coauthors, he is the driving engine behind the social physics agenda, and his work, inspired by his
beginnings as a physicist, is essentially sui generis.
The term embedded systems was introduced by Grofman (1999), but this is only a recent label
for an old and frequently used approach. The hallmark of the embedded systems approach in electoral
systems research is the notion that electoral system effects can be fully understood only within
the context of the overall constitutional, social, and party systems in which they are embedded.
In each of these five areas, important new work has been done in the past decade. Because
one review cannot do justice to this vast and burgeoning literature, I focus on what, in the social
choice literature, would be called vote aggregation mechanisms as my key independent variable.
Vote aggregation mechanisms are the rules that specify how the support for a candidate or party
recorded on the voters’ ballots gets translated into wins and losses. Vote aggregation is only one
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aspect of election design, albeit arguably the most important one. Grofman & Lijphart (1986),
for example, identify nearly two dozen different aspects of electoral rules, including rules affecting
candidate selection processes, campaign finance regulation, and rules about permissible campaign
advertising. However, it is only the rules for vote aggregation that I refer to here when I talk about
“electoral system” effects. As a further means to limit the scope of this article, I make no attempt
to cover the whole field of electoral systems research, and largely limit myself to five research
questions—questions that have long been central to the electoral systems literature.
In the concluding section, I comment on a few very general themes in recent research: the
origins of electoral system choices and changes, the independent impact of electoral rules as
compared to the importance of political context, the distinction between distal and proximal
electoral system effects, and the normative importance of trade-offs across multiple evaluative
criteria. I also consider some recent developments in the investigation of electoral system effects,
such as the use of both field and lab experiments. In summary, although I acknowledge and
applaud the great strides that have been taken in our understanding of the political consequences
of electoral laws in recent decades, I also sound notes of caution about the potential for electoral
engineering given our present state of knowledge.
KEY PROPOSITIONS ABOUT ELECTORAL SYSTEM EFFECTS
Recent electoral systems scholarship is skeptical of a simple dichotomy between proportional representation
(PR) and plurality, and this is a skepticism I share for three reasons. First, there are
parallels between plurality and list PR that are largely neglected in the electoral systems literature
because of the emphasis on a PR versus plurality dividing line or continuum of methods that places
them at opposite poles. In particular, list PR and plurality share the property that they only focus on
first preferences, not overall preference rankings (Grofman 2013, Kurrild-Klitgard 2013). Moreover,
PR and plurality both allow groups with less than majority support to sometimes gain seats,
and this is not true for majoritarian systems. Second, this distinction fails to distinguish among
types of PR, e.g., list PR versus the single transferable vote (STV) versus the single nontransferable
vote (SNTV) versus cumulative voting. Similarly, this distinction fails to distinguish between
plurality and majority systems and among subtypes of each. It also neglects mixed systems, which
have come to be increasingly important both as real-world choices and, for theoretical reasons,
because of features that are thought to be normatively desirable (Shugart & Wattenberg 2001).
Thus, it necessary to acknowledge the complexities of electoral rules and, at mimimum, use
(dummy) variables to distinguish among variants of electoral system types, e.g., open-list versus
closed-list systems; mean district magnitude (i.e., number of seats per district); tiers, rules allowing
pre-electoral coalitions, multistage elections (see e.g., Grofman 2008), and ranked voting methods
(see e.g., Grofman & Feld 2004). However, sometimes for simplicity it is useful to summarize
hypotheses about electoral system effects in tabular form using only the simple PR versus plurality
dichotomy—as I do later in this review.
The electoral systems literature has traditionally focused on five key questions related to party
systems and voter choice: (a) How do electoral systems impact the proportionality of seats–votes
relationships? And, relatedly, are there patterns of bias in translating votes into seats that vary across
rules, e.g., a bias against smaller parties? (b) How do electoral systems affect party proliferation?
(c) How do electoral systems affect the ideological nature of party competition, e.g., the range
of ideological positions represented in the legislature? (d ) How do electoral rules affect voter
turnout? (e) To what extent do governing coalitions or major parties take positions that can be
described as centrist, and how does this affect the degree of match between the preferences of
citizens and the policy choices of the government?
27.4 Grofman
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Other long-studied questions include: How do electoral rules affect cabinet durability and the
stability of policy choices? How does electoral system choice affect the likelihood that countries
will become (and remain) democratic? How does electoral system choice affect the potential for
interethnicaccommodation?Howdo electoral rules impact theextent of descriptiverepresentation
of racial or linguistic groups and of women? How vulnerable are particular electoral systems to
fraud or to other forms of manipulation such as gerrymandering or malapportionment?
More recent literature continues to address these traditional questions but has also examined
other electoral system impacts on governance, such as the ways in which electoral rules affect
the extent of pork-barrel politics, the level of political corruption, and the extent of legislators’
responsiveness to organized or less organized interests or responsiveness to consumers versus
producers. There are also relatively recent theoretically derived and empirically supported claims,
some most fully discussed by economists, about how electoral system choice can impact specific
types of policy outcomes. Examples of such outcomes include the size of government budgets,
the size of the welfare state, the tax structure as it affects inequality reduction, and the extent of
trade protectionism (see Budge & McDonald 2007, Carey & Hix 2012 for political science takes
on some of these issues; cf. Persson & Tabellini 2002). Moreover, there has been renewed interest
in the question of electoral system origins and the reasons for electoral system change.
In the next five sections, I limit myself to the first five of the questions identified above and
evaluate what we now know (or think we know) from both a theoretical and an empirical perspective.
Because of space limitations, I offer only brief comments on the latter three of the five.
Of necessity, I omit much recent work on electoral laws—work covering many important topics,
such as ethnic and gender representation.
HOW DO ELECTORAL SYSTEMS IMPACT THE PROPORTIONALITY
OF SEATS–VOTES RELATIONSHIPS?
Proportionality is only one of many dimensions on which electoral systems can be sorted. For
example,Carey& Shugart (1995) point out that thereareparallels between somePRand somenonPR
systems if we rank them in terms of the incentives to cultivate a personal vote (cf. Grofman &
Bowler 1997, Grofman 2005). Nonetheless, degree of proportionality has been the most common
way in which we distinguish the effects of different voting rules.
In judging proportionality, we may either consider it in the abstract by seeking to rank electoral
systems according to their expected proportionality, or we may look at the degree of proportionality
of seats–votes relationships in actual elections. The measure most often used to characterize
expected proportionality, the threshold of exclusion (TE), has been around since the early 1970s.
Rae et al. (1971) define TE as the largest vote share a party can receive and still be denied any seats
in the district. Using TE involves a hypothetical worst-case scenario in terms of the distribution
of votes among the other parties that will minimize the given party’s seat share.2
TE values have
long been known for most common voting schemes used at the parliamentary level (Lijphart &
Gibberd 1977).
For M-seat districts, in pure list PR systems TE is either exactly or approximately 1/(M + 1).
At the other end of the continuum, for simple plurality and majority systems, TE is (infinitesimally
under) 1/2, regardless of M. Intermediate cases arise for limited voting, where voters have k (single)
2
Paralleling the threshold of exclusion, there is also a threshold of representation, which is the smallest vote share a party can
receive and still win a seat in the district. The threshold of representation involves a hypothetical best-case scenario in terms
of the distribution of votes among the other parties that will maximize the given party’s seat share.
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votes to cast and there are M seats to be filled, k < M, with the M highest vote getters elected. Here
TE is k/(k +M). The closer k is to M, the less proportional is the limited voting rule. Grofman
et al. (2016) provide new results, including a general formula for finding TE for the very large
class of scoring rules that includes the Borda Rule, simple plurality, and the Dowdall rule used for
elections in Nauru.
Although TE is a very important and useful concept, some caveats are in order. First, classifying
rules according to their TE value collapses rules which, in other ways, are quite different. SNTV,
which is limited voting in M-seat districts (M > 1) where voters have but a single vote to cast, is
identical in its TE value to the D’Hondt form of list PR, namely 1/(M + 1). Indeed, TE for singleseat
plurality and for multiseat plurality elections is the same. Second, TE does not directly tell us
the size of the population needed to guarantee control of a seat. Rather, we must take into account
the fact that districts with different values of M also have different populations (Grofman 2001).
Third, TE reflects hypothetical proportionality. As Rein Taagepera (personal communication,
June 4, 2004) observes, “The same electoral rules can lead to vastly different disproportionality,
even in the same country and even in consecutive elections.” To deal with this problem, scholars
commonly calculate empirical indices of disproportionality.
For partisan elections, with vi the vote share of the ith party and si the seat share of that same
party, the two most common measures of overall proportionality are the Loosemore-Hanby index
of distortion (Loosemore & Hanby 1971),
D =
1
2
|vi − si |,
and the Gallagher index (Gallagher 1991),
Gh =
1
2
(vi − si )2
0.5
.
The latter places less weight on disproportionalities among the smaller parties, although, for
obvious reasons, the two indices tend to be highly correlated.
But even when we look at empirical indices of disproportionality, caution is warranted because
what we observe vis-`a-vis proportionality is after the fact. For example, if there is substantial
gerrymandering, then incumbency advantage, especially in districts that have been drawn safe for
one party, may reduce the likelihood of viable challengers and add support to the better-known
incumbent, thus reducing the minority party’s share of the vote. This warning applies especially
to settings that are not fully democratic, where observed disproportionality (or observed party
fragmentation) can be misleading even if there is no overt fraud in the form of ballot stuffing. For
example, until the most recent election, the Singaporean opposition often contested fewer than half
of the constituencies. This happened partly through coercion and partly through electoral rules
that made it hard for them to finance candidacies and field the necessary multiethnic slates, but
largely through the belief that it was hopeless to contest blatantly gerrymandered constituencies
(Tan 2013). Thus, in Singapore, the ratio of opposition vote share to its seat share may seem less
unfair than it really was, because the votes the opposition should have received were never there
to be recorded.
Effects of Increased District Magnitude on Proportionality of Seats and Votes
The link between PR and proportionality is normally assumed to operate via district magnitude.
Theoretically, observed disproportionality should be tied to TE, which for most voting rules
decreases with increasing district magnitude M and thus it should be declining with M. But
27.6 Grofman
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Taagepera & Shugart (1989) show, with cross-national data at the aggregate level, that there
can be compensating effects, i.e., the number of parties competing may rise even faster than M,
leading to a flattening out of disproportionality as M increases. Grofman & Selb (2011) follow up
on this idea using within-nation data for Switzerland and Spain. They show both empirically and
theoretically that, in these PR systems, proportionality does not necessarily increase with district
magnitude, or with an increase in the effective number of parties.3
The effect of district magnitude M can also be important for the proportionality of plurality
rules, but it tends to operate in a way opposite to the expected effects of M on proportionality
in PR systems. Plurality, plurality bloc voting (i.e., plurality in a multiseat setting), and plurality
slate bloc voting (the last of which is a special case of the more general party slate bloc voting)
each yield an expected increase in disproportionality between a party’s vote share and its seat
share as M increases. In plurality bloc voting, each voter has a many votes as there are seats to
be filled, and the candidates with the most votes win. In plurality slate bloc voting, the choice is
between party lists, which win either none of the seats or all of the seats. In the limit, when M
equals all the seats in a legislature, then plurality slate bloc voting in a multiseat setting operates
as a pure winner-take-all system. The exaggeration effect of multiseat plurality on the translation
of votes into seats is generally greater with plurality slate bloc voting than with other forms of
multiseat plurality, because this form rules out the potential for the minority party to elect any of
its candidates if it fails to win the plurality in the district (Tan & Grofman 2014).
Longitudinal Perspectives on Proportionality
The usual way in which we judge proportionality is in terms of seats and votes in a single election.
However, the political geographer Peter J. Taylor (1984) proposed the alternative concept
of “proportional tenure.” Basically, rather than asking how proportional are results in any given
election, recognizing that there may be bias against the smaller party or parties, and also recognizing
that which party is the plurality or majority winner will change over time, Taylor proposed
to average vote and seat shares over a longer time period. Although we can find exceptions, it
is clear that plurality-based rules as a class tend to be more disproportional than PR rules as a
class. Nonetheless, thinking about proportionality in terms of proportional tenure can change
substantially how we evaluate the consequences of particular electoral laws. In the United Kingdom,
where electoral bias has sometimes favored the Conservatives and sometimes Labor (though
always unfavorable to the Liberal Democrats), aggregating across elections reduces the apparent
degree of disproportionality under first-past-the-post. Similarly, our estimates of the degree
of disproportionality in outcomes in the US Congress might change once we recognize that, in
earlier decades, disproportionality in seats and votes appeared to favor Democrats, while now it
appears to favor Republicans.4
HOW DO ELECTORAL SYSTEMS AFFECT PARTY PROLIFERATION?
The central empirical proposition about the link between electoral rules and number of parties is
what has come to be called Duverger’s Law. This has three parts. The first asserts that plurality
3
The effective number of parties (Laakso & Taagepera 1979) is the inverse of the Herfindahl-Hirschman index of fragmentation
and can also be linked to the more familiar concept of variance (Feld & Grofman 2007). For seat share, the effective
number of parliamentary parties is 1/ si
2
. For vote share, the effective number of electoral parties is 1/ vi
2
.
4
There is a useful distinction in the electoral systems literature between partisan bias and disproportionality (see, e.g.,
Grofman 1983). The term partisan bias refers to asymmetry across parties of their translation of seats into votes rather
than proportionality per se.
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COUNTING PARTIES
Although the Laakso–Taagepera (L-T) measure is the “gold standard” for counting number of parties, four recently
proposed alternatives deserve mention, which, for space reasons, I cannot discuss in detail. Dumont & Caulier (2003)
and Kline (2009) independently proposed a modification of the L-T index that the former refer to as the effective
number of relevant parties. It applies the L-T formula to Banzhaf scores (Banzhaf 1965) that are derived from a gametheoretic
approach to voting power. Caulier & Dumont (2010) offer a simpler measure, which is the (normalized)
Banzhaf power score of the largest party stated in terms of its seat share. A third approach is that of Grofman &
Kline (2012), who combine information about the seats or votes distribution of the various parties with information
about where each party is located in ideological/issue space. Finally, Gaines & Taagepera (2013) offer two new ways
to measure the extent to which a given seat or vote distribution reflects a two-party configuration.
facilitates two-party competition; the second states that PR fosters multiparty competition; and
the third makes the same claim for the two-round majority runoff rule. In Duverger’s own words
(1954, p. 228): “The [first-past-the-post] electoral system works in the direction of bipartism; it
does not necessarily and absolutely lead to it in spite of all obstacles. The basic tendency combines
with many others which attenuate it, check it, or arrest it.” One important point about Duverger’s
Law emphasized in all recent work is that it is intended to apply only at the level of individual
constituencies. One can, for example, have two-party competition in each constituency and yet
have more than two parties represented in parliament if competition is not always between the
same two parties at the district level.
Although most of the evidence for the Law is based on the effective number of parliamentary
parties (Laakso & Taagepera 1979) and not the actual number of parties (see e.g., Lijphart 1994;
Iversen & Soskice 2006, table 4; Clark & Golder 2006), there is no doubt that PR systems have
more parties, on average, than plurality ones, no matter how we measure the number of parties
(see sidebar Counting Parties).
In explaining his prediction of two-party competition for plurality elections, Duverger posited a
combination of a mechanical effect (only one party can win in a single-seat constituency, and often
there will be only one other party that is the main challenger) and what he called a psychological
effect, to explain why, in plurality-based competition, parties other than the top two would tend
to be driven out. The posited psychological effect—which I see as better characterized as an
instrumental calculation by voters, generating a form of strategic voting, thus making Duverger
an early rational choice modeler (of the softer form of rational choice)—is that voters desert parties
with no chance of winning. Also we might expect that parties with little chance of electoral success
will have trouble obtaining candidates. However, although we can readily track the effective
number of parties over time, we would need to track individual parties (or the vote choices of
individual voters) to demonstrate that parties that do badly actually tend to go out of business.
Duverger’s Law seems to work well in generating an important contrast between pluralitybased
methods and PR (or the two-round ballot), but there are almost no countries with simple
plurality rules in single-seat constituencies that actually have two-party competition at the district
level, and even fewer with two-party dominance in national parliaments (Grofman et al. 2008a,b;
Bowler et al. 2008). Moreover, we can find PR countries with very few parties (e.g., Austria, until
recently) and some plurality systems with a relatively large number of parties [e.g., some of the
newer democracies in Eastern Europe, especially shortly after the fall of the Soviet Union (Moser
& Scheiner 2013)].
27.8 Grofman
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A number of authors, most notably Cox (1997), have provided reasons why, especially for
plurality-based competition, we might not expect Duverger’s Law to hold. These include the
fact that reliable projections of expected vote share are either not available or are discounted by
supporters of some parties, that there may be more than one competitor who could be regarded
as the “leading” challenger to the winning party, that voters may not differentiate among parties
other than lumping them into the categories of preferred and not preferred, that voter calculations
and the calculations of candidates and parties may be addressed to long-term possibilities and/or
message sending rather than to outcomes in the immediate election, and that parties may be
playing a multilevel game in which they are looking at consequences for their probable success
in other elections (sometime called contamination effects). Moreover, there may be ideological
differences that allow more than two parties to continue to compete, e.g., if one party was the
main challenger on the right flank and another the main challenger on the left flank, or if there
were multiple issue dimensions.
Duverger does not make specific quantitative predictions about the number of parties to be
expected in either PR or two-round ballot systems. Carey & Hix (2011) show that the greatest
marginal gains in proportionality are likely to come as we move from M = 1 to M = 2. Work
using ideas adapted from statistical thermodynamics (see especially Taagepera & Shugart 1989)
makes more specific predictions about how party proliferation will be linked to district magnitude.
Taagepera (2007) offers a synthesis of his lifetime of work in the social physics tradition. I list below
some of his main findings with respect to number of parties and relative party sizes that apply to
what he calls simple systems, i.e., systems in which all districts are the same size, the same voting
rule is used in each, and there are no electoral tiers and no electoral thresholds. Here, when M > 1
it is assumed that we are dealing with a proportional allocation rule rather than with multiseat
plurality.
p = M1/2
n0 = MS1/4
s1 = 1/(n0)1/2
= 1/(MS)1/8
N = (MS) 1/6
,
where S = seats in the legislature, M = seats in the district, p = number of seat-winning parties
in a district, n0 = number of seat-winning parties nationally, si = seat share of the ith largest
party, and N = 1/ (si)2
= Laakso–Taagepera index of effective number of electoral parties.
Taagepera does not try to use his models to explain all variation across districts, across countries,
or over time; nor he does take explained variance as his measure of success. The equations he derives
are good models, in his view, if they require only a handful of theoretically linked variables and if
they successfully fit the average behavior in a large set of observations of electoral system outcomes,
where hypotheses are stated in terms of equations in which the dimensions represented on the
left-hand and right-hand side are the same.
Changes in the Effective Number of Parties Over Time
We might expect that Duvergerian effects would operate to weed out parties that stood no chance
of electoral victory and that, thus, over time, the number of parties would be reduced to what we
might call the carrying capacity of the electoral system. However, as we have seen, Duvergerian
pressures are not the only forces that are operative in the case of plurality contests, and the same is
true more generally. As a consequence, when we examine nations with relatively constant electoral
rules, we can observe considerable variation in the effective number of parties.
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Even the United States had, in much earlier times, more than two political parties, although
the present two-party constellation is more than 150 years old (Bowler et al. 2008). When we
turn to Canada, we find similar variation but no long-term trend toward two-party competition.
Winer et al. (2014) show that, from roughly 1867 until 1898, the graph of the effective number
of parliamentary parties in Canada appeared to be converging toward two. However, from the
Great Depression through World War II and the Korean War, the average effective number of
parliamentary parties at the constituency level varied widely before stabilizing in the post-1960
period at a much higher level (2.6–2.7).
Two-Bloc Politics
Although most work on the number of parties looks at parties individually, especially in systems
where there are pre-electoral coalition possibilities, it is also important to examine the bloc
structure. Various essays in Giannetti & Grofman (2011), comparing the effects of similar but
not identical electoral changes to a mixed system in Japan and Italy that took place in the early
1990s, demonstrate how even small differences in rules can make large differences in outcomes.
For example, in Japan, there was a tendency toward two-party competition after the change in
electoral system, and that had been a desired result. In contrast, in Italy, for nearly two decades,
even after a further change in rules, we saw something like two-bloc politics, where each party
bloc included a large number parties that retained their distinct identity but campaigned jointly
under a common label (Giannetti et al. 2015). Cautres et al. (2016) consider factors that may lead
to two-bloc politics.
Electoral Geography Effects on Party Proliferation
Electoral geography is an important context effect that can create various forms of bias. For
example, although PR can be expected to be more favorable to small parties than plurality or
majoritarian systems, there are some cases—ones where voting strength of particular parties or
groups is geographically concentrated—where the opposite may actually be true (Norris 2004,
p. 44). Also, while the potential for gerrymandering is greater in plurality-based systems than under
PR, especially when there is geographic variation in the electoral strength of different parties (see
Handley & Grofman 2008), there is potential for bias even under PR, and this potential is enhanced
when districts vary in magnitude.
An older literature looks at the intermediating role of racial and ethnic fragmentation on party
fragmentation. Recent research has revisited this question, paying particular attention to electoral
geography (see e.g., Bochsler 2010, Kedar et al. 2014, Lublin 2014, Tan & Grofman 2015).The
bottom line of this literature is that electoral geography can play a powerful role in explaining why
similar rules do not have similar consequences in different polities.
HOW DO ELECTORAL SYSTEMS AFFECT THE IDEOLOGICAL
NATURE OF PARTY COMPETITION?
Downs (1957) demonstrated that, under a particular set of assumptions, plurality-based two-party
competition in single-member districts should tend toward Tweedledum–Tweedledee politics—a
seminal contribution. In contrast, under PR in multiseat districts, we would expect a much wider
ideological range among the parties gaining representation, since parties occupying a relatively
extreme ideological location may nonetheless be able to gain representation.
The basic idea that the ideological range of parties gaining representation in parliament is
greater in PR systems is empirically well supported, but the Downsian notion that, when there
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are only two (major) parties competing, plurality-based elections lead to almost full convergence
between the two party platforms is simply not true, even if it continues to be taught to undergraduates
as gospel. The reason is a simple one. Theorems about electoral system effects (and Downs’s
convergence result is a theorem, even if not stated by Downs in symbolic notation) rest on multiple
assumptions, and many of those assumptions simply do not hold in real-world settings (Grofman
2004). When they do not, then full convergence no longer applies. It is not that Downs was wrong
about there being centripetal forces at work; it is that centrifugal forces are usually present as well,
e.g., party activists with strong policy preferences from whom resources are needed, and party
primaries that may force candidates to cater to their own electoral base. Thus, what we often
get is “moderate convergence” (Adams et al. 2005). However, in the United States, there is not
consistency over time in the degree of convergence of the two parties’ ideological positions.
In the United States, in some time periods, the two major parties are relatively convergent in
policy positions and not very far from the views of the median voter; in other time periods, the
two major parties are highly divergent in policy positions, and neither is close to the views of the
median voter. The pattern of oscillation between moderate convergence and extreme divergence
resembles an accordion’s slow movements in and out, with a time period (half-cycle length) of
about 50 years between its maximal convergence and maximal divergence (see McCarty et al.
2006). Today, as at the end of the 19th century, party differentiation at both the constituency level
and in Congress is extreme. Recent work has attempted to model the factors that can explain why
we observe variation in ideological divergence without any change in electoral system rules (see
Merrill et al. 2014 and Brunell et al. 2016a, b for more extended discussion and literature review).
HOW DO ELECTORAL RULES AFFECT VOTER TURNOUT?
The most commonly studied proposition about the relationship between electoral systems and
turnout asserts that turnout is substantially higher under PR than under plurality. “Empirical
evidence is overwhelming that nationwide turnout is higher on average in proportional representation
(PR) systems than in countries with pluralitarian/majoritarian elections. This finding
survives even when we control for other factors, such as the nature of registration procedures,
weekend voting, compulsory voting, and so on, that also impact turnout” (Grofman & Selb 2011,
p. 94, with internal citations omitted; cf. Franklin 2004, ch. 5).
Andre Blais and his colleagues (see e.g., Blais 2006, Blais & Aarts 2006, cf. Brockington 2004)
call attention to a striking observation about electoral systems and turnout: Even though, ceteris
paribus, PR systems with many parties have higher national-level turnout than single-member
district plurality systems with few parties, turnout does not increase with the effective number of
parties at the national level. This is seen as a puzzle because, as the number of parties increases, so
too should the likelihood that voters can find a party that is ideologically proximate to their own
position,which should incline them to vote rather than abstain. Moreover, we would expect the
number of parties to be correlated with district magnitude (M), and also expect that as M increased
and the threshold of exclusion (TE) fell, the likelihood that some small body of voters would be
able to assure the election of at least one candidate of the party of their first choice would also
increase, thus increasing the incentives for turnout in a different way.
Using within-country data for two countries whose districts vary substantially with respect
to the number of seats being filled, Grofman & Selb (2011) reinforce Blais’s puzzle by showing
that, in these PR systems, turnout does not necessarily increase with district magnitude, once we
move beyond the contrast between M = 1 and M > 1; nor does turnout necessarily increase
with an increase in the effective number of parties. Using a novel approach to measuring political
competition that does not assume all voters have identical turnout incentives (Grofman & Selb
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2009), the authors then seek to explain this puzzle by showing both empirically and theoretically
that competition does not necessarily increase with district magnitude (Grofman & Selb 2011).
Moreover, they emphasize the fact, noted above, that proportionality also does not necessarily
increase with district magnitude past a certain point.
HOW DOES ELECTORAL RULE CHOICE AFFECT CONGRUENCE
BETWEEN CITIZENS’ PREFERENCES AND GOVERNMENT’S
POLICIES?
Consider representative–citizen congruence. Should we expect greater congruence in PR systems
than in plurality ones? If we really thought that plurality systems converged to the preferences of
the median voter, and that, when we had single-seat plurality elections, there would only be two
parties in each district, then we would expect both parties to have identical positions matching
the median in their district, and thus the majority party would be close to the median voter in the
median district. Under these assumptions—ones we know, of course, to be far too simplistic—we
should certainly expect greater congruence in plurality systems than in PR ones. Powell (2000)
found the opposite. However, some more recent work has found that, in more recent time periods,
plurality systems do exhibit greater mean congruence than proportional ones. A third claim, based
on data taken from CSES Module 2 (Dalton et al. 2011, p. 176), is that PR/majoritarian systems
are “about equally effective in representing the median voter.” In their view, “Elections broadly
produce governments that represent the position of their median citizen, and even more clearly
reflect the right–left preferences of their voter,” even though there have been frequent claims that
the structure of the electoral system affects these relationships.
Do these contradictory findings give rise to a puzzle that needs to be explained? My answer
is probably not. On the one hand, time-bound results should be expected, given our previous
discussion of ideological convergence. As noted above, the degree to which parties in the United
States converge in ideological terms has varied greatly over the past 100 or so years despite very
little change in the formal electoral rules. In almost all PR systems, policy outcomes depend on
the coalition structure of the cabinet parties, so in European parliamentary PR systems we should
also expect changes over time in the degree to which governments take policy positions congruent
with their citizenry. This expectation is reinforced by recognizing that recent decades have seen
major changes in party constellations, involving reductions in the strength of mainstream parties
and the rise of fringe parties, especially on the right. We should also note, as Golder & Stamski
(2010, p. 90) point out, “Although the literature examining the relationship between ideological
congruence and electoral rules is quite large, relatively little attention has been paid to how
congruence should be conceptualized. . . . Results regarding ideological congruence can depend
on exactly how scholars conceptualize and measure it.”
SOME LAST REFLECTIONS
Figg-Newton’s Three Laws (A. Wuffle, personal communication, April 1, 2003, quoted in
Grofman 2007):
1. An electoral system once in place tends to stay in place, since there arise around it vested interests
(most notably those who were elected under it) who are supportive of it, and suspicious of any change
that may have (unanticipated) consequences (especially for them).
2. No electoral system exists in a (political) vacuum. The consequences of an electoral system are a
product of the characteristics of the system (such as the threshold of exclusion) and the specific
27.12 Grofman
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socio-political context and political history in which it is embedded. So, no electoral system works
exactly the same way twice, nor do electoral systems export the way we think they might.
3. For every reason to like an electoral system, there is a perhaps near equal and mostly opposite reason
not to like it. Because there are multiple criteria we use to assess theoretical properties and probable
effects, no electoral system is uniformly best.
The authors of the 2012 APSA report were concerned with electoral systems as a tool for
electoral engineering. Thus, their report is, at least in principle, intended to allow us to draw
policy implications and give advice. I offer four caveats about this prospect, following up on ideas
discussed above.
First, although I believe we know far more than we did when I began writing on this topic
40 years ago, I am still skeptical as to how precise our knowledge is about electoral system effects
once we move beyond what Taagepera (2007) calls simple systems to the more complex rules in
actual use (where the devil is in the details). And, in the real world, we have the further complexities
of contingent and contextual effects, especially electoral law’s interactions with other political
institutions and practices.5
There may also be effects of past history, e.g., the kind of selection
effect discussed by Colomer (2004), where the rule is chosen to fit the outcome.
In general, we need to pay more attention to electoral origins in evaluating electoral system
consequences, lest we attribute to electoral systems effects that actually can be traced to forces
shaping both the choice of rules and their apparent consequences (cf. Rogowski 2004, discussing
ideas of Harry Eckstein). For example, in the United States and United Kingdom, we might see
plurality rules and majoritarian institutions originally chosen because these nations are attached
to both majoritarian and individualistic values, and maintained for reasons of both inertia and fit
between value structure and electoral rule. When we confine ourselves to OECD countries, and
we distinguish plurality from two-round majorities, the simple-plurality examples are all Englishspeaking
countries. But then, if we find, say, greater social inequality in these countries than in
(similar) countries with PR electoral rules, we should be very cautious about claiming that the
differences are due to electoral system effects rather than political culture. Also, as Rogowski
(2004) and others have noted, the results that we get for the OECD countries are not always
replicable when we look at the non-OECD democracies.
Second, even if one does not accept the extreme view that electoral systems matter far less than
cultural and contextual factors, one might still expect that, when we change electoral systems, we
may not fully achieve the anticipated political changes unless there has been a change in the social
balance of forces. Otherwise, “the empire will strike back,” acting to negate the impact of the
changes by proceeding with business as usual and/or making compensating adjustments in other
elements of the political process. And the lingering effects of past institutions will take time to
wear off (Giannetti et al. 2015). For example, Scheiner & Tronconi (2011) show that the way in
which campaigns were conducted after Japan changed to a mixed system was strongly affected by
the structure of campaign organization (koenkai ) under the previous SNTV system.
Third, it is important to distinguish between distal and proximal effects. Ferree et al. (2012)
make a compelling case for this in the APSA report. They argue that we need to look at mechanisms,
and that, ceteris paribus, the longer the causal chain between an electoral law and its supposed effects,
the more diluted its effects are likely to be and the harder it will be for us to detect them. All electoral
system effects operate indirectly, through a complex causal chain. Electoral rules impact the nature
5
I am a Goldilocksian with respect to methodology: You are too thick if theoretically grounded generalities never emerge,
and you are too thin if you fail to appreciate case particularities (more generally, see Wuffle 2015).
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Table 1 Some posited tradeoffs between outcomes: plurality versus proportional rules
Plurality elections in single-seat
constituencies
Proportional representation in multiseat
constituencies
Single-party governments:
decisive outcomes and greater government
accountability
direct accountability of individual politicians
to their constituents
greater political stability (?)
fewer ideological extremists in parliament
lower budget deficits (?)
lower taxes (?)
Coalition governments with several political parties:
representation of the entire spectrum of political
views; fewer “wasted” votes
stronger and more cohesive political parties
higher ideological congruence between
government and citizens(?)
proportionality of seats and votes
enhanced representation of women and racial and
ethnic minorities
higher public spending and thus more public
goods and services (?)
lower economic inequality (?)
of voter choice and the options available to voters. They also impact the incentives that structure
party competition, which in turn affect the actual party system constellation. But, in turn, party
systems have implications for whether there will be a coalition government and, if so, what its
structure will be. And the party composition of the cabinet has consequences for the policies that
will be implemented. Other things being equal, the farther we get away from the direct impact of
electoral rules on voter choices, the more likely it is that intervening factors will dilute the impact
of electoral laws.
Fourth, no electoral system can further all normatively desirable goals. If we turn to the normative
goal of electoral engineering, we note good-government goals of various sorts have been
proposed. Some are very general, e.g., fostering democracy, promoting “fair” outcomes in terms of
proportionality and the absence of partisan bias, promoting linkages between the represented and
the representatives; others are more limited but still highly normatively desirable, such as mitigating
ethnic conflict or promoting the representation of women. In the APSA report, Rehfeld et al.
(2012) identify more than a dozen goals we might seek an electoral rule to advance, and I do not
regard that list as exhaustive. But, of course, not all these goals can be simultaneously achieved. A
recurrent theme in the essays in the 2012 APSA report is the need for trade-offs among competing
normatively desirable features. Trade-offs are inevitable because there is no rule that dominates
on all plausible criteria, and there is no clear way to weight the various criteria in order to reach an
overall ranking of rules. Table 1 identifies some of the trade-offs regarding choice of electoral rule
that are alleged in the APSA report. For simplicity, I use the dichotomy of PR rules in multiseat
constituencies versus majoritarian/pluralitarian ones in single-seat constituencies, despite my view
that this dichotomy is inadequate.
Claims about which I am especially skeptical I have marked with a ?, although the most dubious
claims I have simply omitted. Because of space constraints, I discuss only one of the items in the
table: racial and gender representation. Here, let me simply note that, even if we focus on a
single goal, such as descriptive representation, preferential rules such as quotas, reserved seats,
and majority-minority seats directed toward one group may undermine the election of the other
historically marginalized groups that are not targeted (Krook & Moser 2012).
A final note of caution is that electoral engineering can also be a synonym for electoral
manipulation. The in-party can engineer electoral rules for its own advantage, e.g., adopting
plurality slate bloc voting or other forms of party slate bloc voting and then manipulating district
magnitudes to increase the size of its legislative majorities (Tan & Grofman 2015; cf. Birch 2007,
2011; Schedler 2002, 2006).
27.14 Grofman
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DISCLOSURE STATEMENT
The author is not aware of any affiliations, memberships, funding, or financial holdings that might
be perceived as affecting the objectivity of this review.
ACKNOWLEDGMENTS
An earlier and much shorter version of this article was prepared as a memo to Bingham Powell and
Mala Htun as an invited comment on the American Political Science Association’s Presidential
Task Force on Electoral Rules and Democratic Governance. That memo was scheduled to be
presented at a roundtable at the cancelled 2012 APSA Annual Meeting. Research for its preparation
was supported by the Jack W. Peltason Chair in Democracy Studies at the University of California,
Irvine. I wish to dedicate this article to the late Aldo di Virgilio, Professor of Political Science at
the University of Bologna, a scholar of parties and elections who died in 2015 at an age far too
young.
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